Pilot problem dealing with weight and magnitude of force exerted on pilot's body

AI Thread Summary
The discussion focuses on calculating the apparent weight of a pilot during a loop-the-loop maneuver in an airplane, with specific speeds at the top and bottom of the loop. At the top of the loop, the pilot's true weight is 160 lb, and the gravitational force is calculated using the acceleration due to gravity. The normal force exerted by the seat on the pilot's body is questioned, particularly how to incorporate the airplane's velocity into the calculations. The participant seeks clarification on the correct equations to use, specifically whether the equation for normal force, Fn = -mg + mv^2/r, is appropriate. The conversation emphasizes understanding the forces acting on the pilot at different points in the loop.
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Homework Statement


The Pilot of an airplane executes a loop-the-loop manuever in a vertical circle. The airplane's speed is 300 mi/h at the top of the loop and 450 mi/h at the bottom. The radius of the circle is 1200 ft. Use American Engineering units in this problem.

A) The pilot's apparent weight is equal to the magnitude of the force exeted by the seat on his body. What is the pilot's weight at the circle's highest point if his true weight is 160 lb?

B) What is the pilot's apparent weight at the circle's lowest point?

Homework Equations


I know I have to find the some of forces and solve for his weight.


The Attempt at a Solution



I know the first step is to draw a FBD and label the forces acting on the pilot.
At the top of the look, with the pilot traveling 300 mi/hr the forces acting are...

Gravitational Force = mg = 32 ft/s^2
w/Pilot's weight = 32 x 160lb = - 5120
Normal Force of seat = Fn = Fg = 5120 ??

I know I have to factor in the velocity but I am not sure what the equation is that i have to use...
Please help thanks
 
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Is the right equation...

Fn = -mg + mv^2/r ??
 
any help please?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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